APPLICATION OF CIRCLES IN REAL-LIFE SITUATIONS

Solving real life problems involving circles

1. Precalculus Science, Technology, Engineering, and Mathematics Lesson 1.4 Applications of Circles in Real-life Situations

2. 2 A wheel is one of the manifestations of circles in real-life. It remains one of the most important inventions of all time.

3. 3 The properties of a circle made it possible for vehicles to move from one place to another. It is also present in engines and road designs. GPS can also determine distance using circles. In this lesson, we will focus on solving word problems involving circles.

4. 4 How do we solve word problems involving circles?

5. 5 Solve situational problems involving circles.

6. 6 Apply the concepts related to circle in solving word problems. Solve word problems involving circles.

7. 7   Recall: Standard Form of the Equation of a Circle

8. 8 where the numerical coefficients are real numbers and   Recall: General Form of the Equation of a Circle

9. 9 The viewers in this library at Phillips Exeter Academy in New Hampshire can immediately see the stacks of books in each floor. Applications of Circles

10. 10 The circular shape of wheels makes it possible for vehicles to move fast and smoothly. Applications of Circles

11. 11 Camera lenses makes it easier for zoom and focus rotation. Applications of Circles

12. 12 In solving word problems involving circles, it is important that we know the different parts of the circle and how to graph them. Illustrations can also be helpful by visualizing the given problem. Solving Word Problems Involving Circles

13. 13 A cellular tower is located at on a coordinate plane whose units represent miles. It is designed to service an 11-mile radius. Identify the standard equation of the outer boundary of the region serviced by the tower.  

14. 14 A cellular tower is located at on a coordinate plane whose units represent miles. It is designed to service an 11-mile radius. Identify the standard equation of the outer boundary of the region serviced by the tower.    

15. 15 15 A Wi-Fi router placed at on a coordinate plane whose units represent meters can reach up to 25 meters in radius. Find the equation in standard form of the outer boundary of the region reached by the router.  

16. 16 The sprinkler placed at a garden covers 12 ft around it. The equation of the outer boundary reached by the sprinkler is given by . Find the location of the sprinkler on a coordinate plane.  

17. 17 The sprinkler placed at a garden covers 12 ft around it. The equation of the outer boundary reached by the sprinkler is given by . Find the location of the sprinkler on a coordinate plane.    

18. 18 18 The outer rim of a Ferris wheel is represented by the equation . Identify the center of the Ferris wheel.  

19. 19 A radio tower is located at and has a range of 15 km. The lettered points on the coordinate plane represent the cities around it. Find the equation of the circle that represents the coverage of the radio tower and sketch the circle. Which among the cities are out of coverage of the radio tower?  

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21. 21 A radio tower is located at (20,15) and has a range of 15 km. The lettered points on the coordinate plane represent the cities around it. Find the equation of the circle that represents the coverage of the radio tower and sketch the circle. Which among the cities are out of coverage of the radio tower? T he cities C, D, and G are the cities outside the coverage of the radio tower.

22. 22 Sketch of the circle:

23. 23 23 A volcano is located at on a coordinate plane. The lettered points on the coordinate plane represent the cities around it. The government reminds those cities around the 14-km radius of the volcano to take precautionary measures in case of emergency.  

24. 24 24 Find the equation of the circle that represents the range of the volcano and sketch the circle. Which among the cities are outside the 14-km radius of the volcano?

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26. 26 How is the concept of graphing circles helpful in solving situational problems involving circles?

27. 27 Refer to the given problem below. A hospital is designated to offer service to the cities under its 13-km radius. The lettered points on the coordinate plane represent the cities around it.

28. 28 Identify the following: location of the hospital sketch of the circle cities within the service of the hospital

29. 29 Solve the following problems, then sketch the graph. Tricia is watering the plants in their garden circularly using a water hose. She is watering the plants without leaving her position at . The location of the farthest plant that the water can reach is at . Find the range of the water hose in feet and determine the standard form of the equation of the circle.  

30. 30 Solve the following problems, then sketch the graph. A lighthouse is located at the origin. The beam of the lighthouse can be seen up to 15 miles, and you are on a ship that is 8 miles east and 10 miles north of the lighthouse. Will you be able to see the lighthouse beam? Determine the standard and general form of the equation of the circle.

31. 31 To solve situational problems involving circles: Use the method of completing the square to determine the location of the center given the general form of the equation of the circle.

32. 32 To identify the equation of a circle given its center and radius, use the standard form of the equation of a circle. In finding the radius given the center and a point on a circle, use the distance formula.

33. 33 33 The ringing of the church bell signifies the start of a mass. It can be heard up to a radius of 28 meters. If Sofia’s house is 25 meters east and 15 meters south of the church, which is at the origin, will they be able to hear the bell from their house? Explain your answer.

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